Question

Given: ΔABC ~ ΔDEF and Prove: slope of AB × slope of DE = -1

Statements/Reasons:

ΔABC is similar to ΔDEF (Given)
Property of similar triangles
slope of AB = slope of DE (Definition of slope)
slope of AB × slope of DE (Multiplying the slopes)
slope of AB × slope of DE = -1 (Simplifying the right side)
Substitution property of equality
What is the missing statement in step 5?

a) slope of DE = -1
b) slope of AB = 1
c) slope of DE × slope of AB = 1
d) slope of DE × slope of AB = -1

Answer 1

The missing statement in step 5 necessary to prove that the slope of line AB multiplied by the slope of line DE equals -1 is not provided in the given information, as additional conditions about the lines' relationship are required to reach this conclusion.

Step-by-step explanation:

The missing statement in step 5 of proving that the slope of AB multiplied by the slope of DE equals -1 is not explicitly given in the options. However, if we are trying to prove that these slopes are negative reciprocals of each other (which would make their product -1), then we would need additional information that is not available in the provided statements. The properties of similar triangles and the definition of the slope would not suffice to prove that one slope is the negative reciprocal of the other without knowing the relationship between the specific lines AB and DE. For instance, we would need information about the lines being perpendicular to establish that their slopes' product is -1.